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In a smoking survey among boys between the ages of 12 and
Chapter 4, Problem 4.1-8(choose chapter or problem)
In a smoking survey among boys between the ages of 12 and 17, \(78 \%\) prefer to date nonsmokers, \(1 \%\) prefer to date smokers, and \(21 \%\) don’t care. Suppose seven such boys are selected randomly. Let \(X\) equal the number who prefer to date nonsmokers and \(Y\) equal the number who prefer to date smokers.
(a) Determine the joint pmf of \(X\) and \(Y\). Be sure to include the support of the pmf.
(b) Find the marginal pmf of \(X\). Again include the support.
Questions & Answers
QUESTION:
In a smoking survey among boys between the ages of 12 and 17, \(78 \%\) prefer to date nonsmokers, \(1 \%\) prefer to date smokers, and \(21 \%\) don’t care. Suppose seven such boys are selected randomly. Let \(X\) equal the number who prefer to date nonsmokers and \(Y\) equal the number who prefer to date smokers.
(a) Determine the joint pmf of \(X\) and \(Y\). Be sure to include the support of the pmf.
(b) Find the marginal pmf of \(X\). Again include the support.
ANSWER:Answer:
Step 1 of 2 :
Given,
In a smoking survey among boys between the ages of 12 and 17.
Here 78% prefer to date non smokers.
78% = 0.78
1% prefer to date smokers.
1% = 0.01 and
21% don’t care.
21% = 0.21
We know that seven boys are selected randomly.
Let X equal the number who prefer to date non smokers and
Let Y equal the number who prefer to date smokers .
PMF(x,y) = Prob {X prefer non smokers, Y prefer smokers}
Our goal is to find
a). Determine the joint pmf of X and Y.Be sure to include the support of the pmf.
b).Find the marginal pmf of X.Again include the support.
a).
Now we have to determine the joint pmf of X and Y.
We know that prefer to date non smokers is 0.78, prefer to date smokers is 0.01,don’t care is 0.21 and n=7.
Then the joint pmf X and Y is
Where
Hence the the joint pmf of X and Y is above.